Violet Parker was last seen in the Northumberland Avenue area of Shepway in an agitated state, before she left an address on foot.
The 56-year-old is described as being white, five feet tall, of slim build and with long blonde hair. She was wearing a pink onesie and blue tasselled sandals when she was last seen.
Inspector Neil Maudhub said: ‘We are urgently seeking to locate Violet as we are particularly concerned for her welfare.
‘It is thought she may be in possession of a bladed article and we are asking anyone who sees her to call us immediately but not to approach her.’
Anyone who sees Violet or knows where she might be is urged to call 999, quoting 4-0979.